I wholeheartedly agree with this woman's policy. Unfortunately, there was no way to pay her to increase her methods. Some undisciplined child who is likely a future criminal has asked me to eliminate her because he has a problem with law and order. But Grelod the Kind seems like she would get along with the Dark Brotherhood. Will killing her alert the DB to my willingness to help them, or will it anger them and send another DB assassin after me?

What??

nothing about grelod suggests she is favorable to the dark brotherhood. they are an elite league of entropy-worshipping assassins; she is a simple bully.

You mean like all the children she is taking "care" of? Because she refuses to let them be adopted into loving homes and says she will throw them out on the street when they turn 18. She is creating future criminals all by herself.